TY - JOUR

T1 - Model calculations for 50Ca and the convergence properties of the perturbation expansion for the effective interaction

AU - Barrett, Bruce R.

AU - Weng, Wu Tsung

AU - Osnes, Eivind

AU - Richert, Jean

N1 - Funding Information:
t Work supported in part by the NSF, Grant GP-39030X1.

PY - 1975/9/1

Y1 - 1975/9/1

N2 - Using the results of the "exact" shell-model calculation of McGrory et al. for the Ca isotopes as "experimental data", we performed model calculations for 50Ca in order to test the convergence properties of different perturbation schemes for computing the effective interaction V. As such, our aim was not to describe the physical spectrum of 50Ca. Three different model spaces were investigated: (i) p 3 2 (ii) p 3 2 + p 1 2 and (iii) p 3 2 + p 1 2 + f 5 2. In the p 3 2 model space three different first-order interactions were used in computing the perturbation expansion for V through third order: (a) V ≡ {G + G}3p-1hKB, (b) a standard G-matrix computed from V in (a), and (c) a doubly partitioned G-matrix computed from V by excluding excitations into the p 1 2level. The results for the doubly partitioned G yielded the best convergence through third order and the best agreement with the J = 0, T = 1 ground state of 50Ca. The core polarization was found to be repulsive for a pure T = 1 system, so that certain third-order terms did not cancel against the large vertex renormalization terms in our special case. The [2, 1] padé approximant for each interaction appeared to indicate reasonable convergence in all three cases through third order. The results for the expanded (p 3 2 + p 1 2) and (p 3 2 + p 1 2 + f 5 2) model spaces were difficult to interpret in a meaningful way, because of small energy denominators. Our results would indicate that one should compute in a doubly partitioned space when there are single-particle levels lying close in energy to the model space levels.

AB - Using the results of the "exact" shell-model calculation of McGrory et al. for the Ca isotopes as "experimental data", we performed model calculations for 50Ca in order to test the convergence properties of different perturbation schemes for computing the effective interaction V. As such, our aim was not to describe the physical spectrum of 50Ca. Three different model spaces were investigated: (i) p 3 2 (ii) p 3 2 + p 1 2 and (iii) p 3 2 + p 1 2 + f 5 2. In the p 3 2 model space three different first-order interactions were used in computing the perturbation expansion for V through third order: (a) V ≡ {G + G}3p-1hKB, (b) a standard G-matrix computed from V in (a), and (c) a doubly partitioned G-matrix computed from V by excluding excitations into the p 1 2level. The results for the doubly partitioned G yielded the best convergence through third order and the best agreement with the J = 0, T = 1 ground state of 50Ca. The core polarization was found to be repulsive for a pure T = 1 system, so that certain third-order terms did not cancel against the large vertex renormalization terms in our special case. The [2, 1] padé approximant for each interaction appeared to indicate reasonable convergence in all three cases through third order. The results for the expanded (p 3 2 + p 1 2) and (p 3 2 + p 1 2 + f 5 2) model spaces were difficult to interpret in a meaningful way, because of small energy denominators. Our results would indicate that one should compute in a doubly partitioned space when there are single-particle levels lying close in energy to the model space levels.

UR - http://www.scopus.com/inward/record.url?scp=49549147917&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=49549147917&partnerID=8YFLogxK

U2 - 10.1016/0375-9474(75)90522-9

DO - 10.1016/0375-9474(75)90522-9

M3 - Article

AN - SCOPUS:49549147917

VL - 248

SP - 429

EP - 440

JO - Nuclear Physics A

JF - Nuclear Physics A

SN - 0375-9474

IS - 3

ER -